Higher-order theory of homogeneous plate flexure

Abstract

The need for higher-order model to obtain accurate estimates to transverse shear and normal stresses and strains is well known. In this paper, higher order deformation theory with provision for cubic variation of in-plane displacements and parabolic variations of the normal displacement has been considered for detailed study. Numerical results have been obtained for infinite plate strip, simply supported on opposite edges and infinitely long in the other direction, subjected to sinusoidal static load. Displacements, strains and stresses are compared with the exact solution. Results by the classical plate theory, Levinson's theory and a higher- order theory based on partial deflections are also included. This study shows that the present model can predict all displacements, strains, and stresses reasonably accurately. Further, it is also noted that the statically equivalent estimates to transverse stresses from classical theory and the corresponding strains also agree closely with the exact solution.